This patent pertains to numbers and numbering systems. It is fair to say that the concept of a numerical system has been around for a while. Indeed, associating a number with a quantity is very literally an age old practice. While systems have varied, most are based upon ten different numbers. This commonality is attributable to the fact that humans have ten combined fingers (i.e., digits) on their two hands. The most obvious example of a system based upon ten digits is the decimal system (i.e., possible single digit numbers are 0 through 9). However, while base ten systems are the most popular, other systems (e.g., binary, octal, and hexadecimal) are equally effective mathematically, and preferable in certain cases.
One such case is that of the typical computer system. Computer systems do not (typically) have fingers or digits. Instead they rely upon different voltage levels to represent different numbers. From a design and cost perspective, it is much easier to represent two different numbers (i.e., 0 and 1) than it is to represent ten different numbers (i.e., 0 through 9). Therefore the binary number system (i.e., base 2) is used to internally represent numbers in most computer systems. An extension to the binary numbering system is a standard that is referred to as the Binary Floating Point Standard (IEEE 754-1985). This standard is an agreed upon way to represent multi-digit numbers in binary.
When the computer system's internally represented binary numbers are presented to the user, they are typically converted into base 10 so that they can be more easily understood. Some base 2 numbers, though, do not convert well to base 10 because the conversion results in an indefinitely repeating fraction. Said another way, for certain base 2 numbers, the conversion from base 2 to base 10 introduces rounding error. For this reason, the standards community is at work developing a new decimal floating point standard (IEEE-SA 754R).
Included within this standard is the notion of a cohort. Unlike binary floating-point formats, a number may have multiple representations in the new decimal floating-point format. The set of floating-point representations a number maps to is called the number's cohort. Said another way, the members of a cohort are distinct representations of the same number. For example: 2.0, 2.00, and 2.000, are three representations of the same number and are members of the same cohort. These different representations are permitted because they have significance to some computer system users. For example, a measurement of 2.0 grams to a chemist has a different meaning than a measurement of 2.000 grams. Specifically, the chemist knows that a measurement of 2.000 grams means that the item weighs between 1.9995 and 2.0005 grams, whereas a measurement of 2.0 means it weighs between 1.95 and 2.05 grams. This notion is known as precision.
While it is clear that the use of cohorts within the standard provides value, this value is not without cost. The cost is associated with accessing cohorts stored in a database. As is well-known, there are many different types of databases, but the most common is usually called a relational database. A relational database organizes data in tables that have rows, which represent individual entries or records in the database, and columns, which define what is stored in each entry or record. Each table has a unique name within the database and each column has a unique name within the particular table. Most databases also use indexes, which are very important data structures that inform the database management system of the location of a certain row in a table (or tables) given an indexed column value, analogous to a book index informing the reader on which page a given word appears. Thus each distinct column value in the table appears in the index along with the location of all of the rows containing that value. Database indexes are important because they are used to speed access to the database. Of course, when the database performs better, the computer system performs better, and when the computer system performs better, the computer system's users are more satisfied, which of course translates into more sales for the computer system maker.
The specific problem addressed in this patent is the fact that the notion of a cohort introduces multiple column values for the same number into the database index. Taking the above example, three different rows respectively containing the numbers 2.0, 2.00, and 2.000 would each be represented individually in the database index. Thus, the computer system will need to consider multiple database index entries to locate all the values that are mathematically equivalent to 2.0, which slows performance. Of course, individuals interested in the precision of the various numbers would appreciate this indexing approach because the database remains efficient for them. The issue, though, is that most computer system users are not interested in the differences between 2.0, 2.00, and 2.000. To them a 2 is a 2 is a 2. Thus, from a performance perspective, the introduction of the notion of a cohort penalizes the many in favor of the few.
Without an improved system, the value associated with use of cohorts, as set forth in IEEE-SA 754R, will continue to be diminished by the performance costs levied upon the majority of computer system users.